# install.packages("devtools")
# devtools::install_github("emitanaka/edibble", force = T)
# devtools::install_github("emitanaka/deggust", force = T)
if (!require("pacman")) install.packages("pacman")
pacman::p_load(readxl, agricolae, agricolaeplotr, car, tidyverse, PMCMRplus, outliers, nortest, mvtnorm, lmtest, ExpDes, edibble, gt,
gtsummary, devtools, deggust, xlsx, desplot,
ggResidpanel, fastGraph, gvlma,
ScottKnott, kSamples, psych)
Sesión 04
Diseño Cuadrado Latino
Christian Vásquez-Velasco, Bach., M.Sc.(c)
InkaStats Academy
2023
[Curso: Métodos Estadísticos para Experimentos Agrícolas en R]
Planeamiento
Instalar paquetes necesarios
Crear un libro con el paquete agricolae
Sketch del diseño
Sketch codificado del diseño
Guardar el libro generado
Libro de campo
Guardar el libro de campo generado
agricolaeplotr::plot_latin_square(design = salida,
factor_name = "variedades",
reverse_y = TRUE,
reverse_x = FALSE) +
labs(fill = "Variedades",
x = "Columnas",
y = "Filas",
title = "Diseño Cuadrado Latino",
subtitle = "Rendimiento de cultivos",
caption = "Curso: Métodos Estadísticos para Experimentos Agrícolas en R - 2023") +
theme_classic()
Crear un libro de campo con el paquete edibble
Análisis del diseño
Importación de datos
Creación del modelo lineal
Definición del modelo
\[Y = \beta_0 + \beta_1*T_B + \beta_2*T_C + \beta_3*T_D + \beta_4*T_E + \beta_5*F{2} + \beta_6*F{3} + \beta_7*F{4} + \beta_8*F{5} + \beta_9*C{2} + \beta_{10}*C{3} + \beta_{11}*C{4} + \beta_{12}*C{5} + \epsilon\]
\[\hat{Y} = \beta_0 + \beta_1*T_B + \beta_2*T_C + \beta_3*T_D + \beta_4*T_E + \beta_5*F{2} + \beta_6*F{3} + \beta_7*F{4} + \beta_8*F{5} + \beta_9*C{2} + \beta_{10}*C{3} + \beta_{11}*C{4} + \beta_{12}*C{5}\]
Call:
lm(formula = rdt ~ trt + F + C, data = data)
Residuals:
Min 1Q Median 3Q Max
-2.9796 -0.9756 0.1684 0.7484 3.1784
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 44.670 1.567 28.515 2.15e-12 ***
trtB 4.584 1.374 3.336 0.00593 **
trtC 8.594 1.374 6.255 4.22e-05 ***
trtD 12.034 1.374 8.759 1.47e-06 ***
trtE 11.744 1.374 8.548 1.90e-06 ***
FF2 2.152 1.374 1.566 0.14326
FF3 -1.864 1.374 -1.357 0.19985
FF4 -1.576 1.374 -1.147 0.27371
FF5 3.154 1.374 2.296 0.04052 *
CC2 1.862 1.374 1.355 0.20031
CC3 2.006 1.374 1.460 0.16996
CC4 2.864 1.374 2.085 0.05915 .
CC5 3.724 1.374 2.710 0.01894 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.172 on 12 degrees of freedom
Multiple R-squared: 0.921, Adjusted R-squared: 0.8419
F-statistic: 11.65 on 12 and 12 DF, p-value: 7.933e-05Conclusión: Se concluye que los coeficientes \(\beta_0\), \(\beta_1\), \(\beta_2\), \(\beta_3\), \(\beta_4\), \(\beta_8\), \(\beta_12\) correspondientes a los tratamientos B, C, D y E, a la fila 5 y columna 5 respectivamente, fueron estadísticamente distintos de 0. El ajuste del modelo descrito en el \(R^2\) fue de 0.921, lo que quiere decir que el 92.1 % de la varianza del rendimiento está explicado por las variables Tratamiento, Fila y Columna.
Verificación visual de los supuestos del modelo
Influence measures of
lm(formula = rdt ~ trt + F + C, data = data) :
dfb.1_ dfb.trtB dfb.trtC dfb.trtD dfb.trtE dfb.FF2 dfb.FF3
1 1.5219 -1.07e-16 3.48e-16 5.77e-16 1.08e+00 -1.08e+00 -1.08e+00
2 -0.0391 -7.48e-17 -7.43e-02 -4.18e-18 -2.87e-17 -7.43e-02 -7.26e-18
3 -0.5548 -1.05e+00 7.63e-16 2.26e-16 -1.57e-16 6.22e-16 -1.05e+00
4 -0.3441 2.45e-01 2.45e-01 2.45e-01 2.45e-01 7.77e-17 1.41e-16
5 0.1609 1.61e-17 2.19e-17 3.06e-01 -3.62e-17 3.15e-17 -4.38e-17
6 0.3081 -2.20e-01 -2.20e-01 -2.20e-01 -2.20e-01 -2.20e-01 -2.20e-01
7 -0.0176 3.06e-17 1.79e-17 5.01e-02 5.49e-18 5.01e-02 2.82e-17
8 -0.0469 4.17e-17 1.34e-01 2.45e-17 9.38e-18 -2.32e-17 1.34e-01
9 -0.0616 1.75e-01 -5.68e-17 -8.73e-18 -1.08e-17 -1.20e-17 2.52e-17
10 0.2180 3.27e-17 4.45e-17 0.00e+00 -6.21e-01 6.23e-17 -2.61e-17
11 -0.1284 8.46e-18 -2.44e-01 -5.90e-17 -1.05e-16 2.44e-01 2.44e-01
12 -0.4084 1.16e+00 -4.90e-16 3.30e-17 -1.02e-16 1.16e+00 1.52e-18
13 0.1012 -1.26e-16 -1.45e-16 -2.88e-01 -7.72e-17 -8.00e-17 -2.88e-01
14 0.1009 2.46e-17 1.46e-17 4.37e-17 -2.88e-01 -1.51e-17 -2.06e-17
15 -0.0612 1.16e-01 1.16e-01 1.16e-01 1.16e-01 -6.53e-17 -5.40e-17
16 -0.3266 -6.21e-01 -1.85e-16 -2.07e-16 -2.67e-16 6.21e-01 6.21e-01
17 0.1322 -9.79e-17 2.70e-17 0.00e+00 -3.77e-01 -3.77e-01 3.76e-17
18 0.3959 -7.52e-01 -7.52e-01 -7.52e-01 -7.52e-01 1.57e-16 7.52e-01
19 -0.0770 4.65e-17 9.44e-17 2.20e-01 2.99e-17 4.23e-17 4.72e-17
20 -0.0172 6.79e-18 4.89e-02 1.39e-18 -4.29e-18 -6.88e-18 -1.03e-18
21 -0.1521 -3.76e-17 -3.11e-16 -2.89e-01 -1.46e-16 2.89e-01 2.89e-01
22 -0.2997 5.69e-01 5.69e-01 5.69e-01 5.69e-01 -5.69e-01 -5.41e-17
23 -0.1230 6.35e-17 7.69e-17 8.00e-17 3.51e-01 -6.08e-17 3.51e-01
24 -0.0469 1.85e-17 1.34e-01 -2.70e-17 -2.46e-17 -2.80e-17 -1.92e-17
25 -0.1232 3.51e-01 -7.86e-17 4.39e-18 -7.40e-17 1.46e-16 2.22e-16
dfb.FF4 dfb.FF5 dfb.CC2 dfb.CC3 dfb.CC4 dfb.CC5 dffit cov.r
1 -1.08e+00 -1.08e+00 -1.08e+00 -1.08e+00 -1.08e+00 -1.08e+00 2.473 0.0296
2 2.52e-18 -3.26e-19 7.43e-02 7.43e-02 7.43e-02 7.43e-02 -0.169 6.2578
3 3.18e-16 1.85e-17 1.05e+00 1.05e+00 1.05e+00 1.05e+00 -2.404 0.0378
4 -2.45e-01 7.96e-17 2.45e-01 2.45e-01 2.45e-01 2.45e-01 -0.559 4.6111
5 0.00e+00 3.06e-01 -3.06e-01 -3.06e-01 -3.06e-01 -3.06e-01 0.697 3.8386
6 -2.20e-01 -2.20e-01 2.20e-01 -1.76e-16 -1.41e-16 -1.40e-16 0.501 4.9256
7 2.21e-17 2.37e-17 5.01e-02 1.23e-17 9.26e-18 3.30e-18 0.114 6.3655
8 9.85e-18 1.06e-17 1.34e-01 5.47e-17 6.20e-17 7.33e-17 0.305 5.8371
9 1.75e-01 -3.23e-17 1.75e-01 8.16e-17 9.33e-17 1.23e-16 0.400 5.4280
10 1.89e-16 -6.21e-01 -6.21e-01 2.23e-17 -1.34e-18 6.82e-17 -1.417 0.8533
11 2.44e-01 2.44e-01 -1.27e-16 -2.44e-01 -2.41e-17 -4.82e-17 -0.556 4.6262
12 1.58e-17 -6.13e-17 -1.21e-16 1.16e+00 3.57e-17 -1.28e-16 2.655 0.0154
13 -9.85e-18 -7.34e-17 -1.20e-16 -2.88e-01 -1.91e-16 -1.96e-16 -0.658 4.0624
14 -2.88e-01 2.53e-18 4.99e-17 -2.88e-01 -4.23e-17 -1.89e-17 -0.656 4.0702
15 -6.19e-17 -1.16e-01 1.21e-17 -1.16e-01 1.88e-17 3.32e-17 -0.265 5.9806
16 6.21e-01 6.21e-01 -1.29e-16 0.00e+00 -6.21e-01 0.00e+00 -1.415 0.8570
17 8.83e-17 8.93e-17 6.54e-17 0.00e+00 -3.77e-01 4.14e-17 -0.859 2.9544
18 2.03e-16 1.52e-16 -1.96e-16 -5.39e-17 7.52e-01 -8.25e-17 1.716 0.3662
19 2.20e-01 4.43e-17 8.85e-17 1.10e-16 2.20e-01 9.15e-17 0.501 4.9256
20 7.44e-18 4.89e-02 1.28e-17 1.05e-17 4.89e-02 1.07e-18 0.112 6.3697
21 2.89e-01 2.89e-01 -1.65e-16 -9.14e-17 -8.79e-17 -2.89e-01 -0.659 4.0545
22 -7.22e-17 2.00e-17 -2.09e-17 -1.20e-17 8.66e-17 -5.69e-01 -1.299 1.1557
23 -7.65e-17 -2.77e-17 -1.46e-16 0.00e+00 0.00e+00 3.51e-01 0.800 3.2734
24 1.34e-01 1.29e-17 -1.86e-17 1.63e-17 2.03e-17 1.34e-01 0.305 5.8371
25 2.14e-16 3.51e-01 8.62e-18 5.19e-17 8.01e-17 3.51e-01 0.801 3.2656
cook.d hat inf
1 0.33917 0.52 *
2 0.00240 0.52 *
3 0.32660 0.52 *
4 0.02556 0.52 *
5 0.03921 0.52
6 0.02061 0.52 *
7 0.00109 0.52 *
8 0.00773 0.52 *
9 0.01326 0.52 *
10 0.14417 0.52
11 0.02532 0.52 *
12 0.37164 0.52 *
13 0.03501 0.52
14 0.03487 0.52
15 0.00587 0.52 *
16 0.14387 0.52
17 0.05837 0.52
18 0.19808 0.52
19 0.02061 0.52 *
20 0.00104 0.52 *
21 0.03516 0.52
22 0.12395 0.52
23 0.05091 0.52
24 0.00773 0.52 *
25 0.05108 0.52 
Cumplimiento de supuestos del modelo lineal general
Independencia de residuos
\(H_0: \text{Los residuos del rendimiento son completamente aleatorios e independientes}\)
\(H_1: \text{Los residuos del rendimiento no son completamente aleatorios e independientes}\)
Durbin-Watson test
data: modelo.dcl
DW = 1.753, p-value = 0.2041
alternative hypothesis: true autocorrelation is not 0Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, los residuos del rendimiento son completamente aleatorios e independientes.
Normalidad de residuos
\(H_0: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)
\(H_1: \text{La distribución de los residuos del rendimiento es similar a la función normal}\)
Shapiro-Wilk normality test
data: rstudent(modelo.dcl)
W = 0.96303, p-value = 0.4782
Anderson-Darling normality test
data: rstudent(modelo.dcl)
A = 0.38392, p-value = 0.3688
Exact one-sample Kolmogorov-Smirnov test
data: rstudent(modelo.dcl)
D = 0.10352, p-value = 0.9264
alternative hypothesis: two-sided
Cramer-von Mises normality test
data: rstudent(modelo.dcl)
W = 0.054267, p-value = 0.4357
Pearson chi-square normality test
data: rstudent(modelo.dcl)
P = 7.96, p-value = 0.1585Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la distribución de los residuos del rendimiento es similar a la función normal o gaussiana.
Homocedasticidad
\(H_0\): La varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.
\(H_1\): La varianza del rendimiento no es constante con respecto a los valores ajustados del rendimiento.
Non-constant Variance Score Test
Variance formula: ~ fitted.values
Chisquare = 0.915634, Df = 1, p = 0.33862
studentized Breusch-Pagan test
data: modelo.dcl
BP = 15.008, df = 12, p-value = 0.241
Breusch Pagan Test for Heteroskedasticity
-----------------------------------------
Ho: the variance is constant
Ha: the variance is not constant
Data
-------------------------------
Response : rdt
Variables: fitted values of rdt
Test Summary
---------------------------
DF = 1
Chi2 = 0.915634
Prob > Chi2 = 0.338624 Conclusión. A un nivel de significancia de 0.1, se concluye que no existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, la varianza del rendimiento es constante con respecto a los valores ajustados del rendimiento.
Recomendación. Debido a que se cumple con el supuesto de homocedasticidad, para evaluar los efectos de los tratamientos con respecto al rendimiento, se debe proceder a realizar el análisis de varianza.
Estadísticas globales
Call:
lm(formula = rdt ~ trt + F + C, data = data)
Coefficients:
(Intercept) trtB trtC trtD trtE FF2
44.670 4.584 8.594 12.034 11.744 2.152
FF3 FF4 FF5 CC2 CC3 CC4
-1.864 -1.576 3.154 1.862 2.006 2.864
CC5
3.724
ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance = 0.05
Call:
gvlma(x = .)
Value p-value Decision
Global Stat 3.3051 0.5081 Assumptions acceptable.
Skewness 0.3324 0.5642 Assumptions acceptable.
Kurtosis 0.0817 0.7750 Assumptions acceptable.
Link Function 1.7360 0.1876 Assumptions acceptable.
Heteroscedasticity 1.1550 0.2825 Assumptions acceptable.Análisis de varianza
\[Y = \mu + \tau_{i} + \beta_{j} + \gamma_{k} + \epsilon_{ijk}\]
\[\hat{Y} = \mu + \tau_{i} + \beta_{j} + \gamma_{k}\]
Para los tratamientos:
\(H_0: \tau_{A} = \tau_{B} = \tau_{C} = \tau_{D} = \tau_{E} = 0\)
\(H_1: \text{En al menos un tratamiento el } \tau \text{ es diferente a los demás.}\)
\(H_1: \tau_i \neq 0\text{; en al menos un tratamiento.}\)
Para las filas:
\(H_0: \beta_{1} = \beta_{2} = \beta_{3} = \beta_{4} = \beta_{5} = 0\)
\(H_1: \text{En al menos una fila el } \beta \text{ es diferente a los demás.}\)
\(H_1: \beta_j \neq 0\text{; en al menos una fila.}\)
Para las columnas:
\(H_0: \gamma_{1} = \gamma_{2} = \gamma_{3} = \gamma_{4} = \gamma_{5} = 0\)
\(H_1: \text{En al menos una columna el } \gamma \text{ es diferente a los demás.}\)
\(H_1: \gamma_k \neq 0\text{; en al menos un columna.}\)
Analysis of Variance Table
Response: rdt
Df Sum Sq Mean Sq F value Pr(>F)
trt 4 522.30 130.574 27.6685 5.619e-06 ***
F 4 99.20 24.801 5.2553 0.0111 *
C 4 38.48 9.620 2.0385 0.1527
Residuals 12 56.63 4.719
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Conclusión. A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula, por lo tanto, al menos un tratamiento tiene un efecto sobre el rendimiento estadísticamente diferente del resto de tratamientos.
Comparaciones de medias
- A vs B:
\(H_0: \mu_{A} - \mu_{B} = 0\)
\(H_1: \mu_{A} - \mu_{B} \neq 0\)
- A vs C:
\(H_0: \mu_{A} - \mu_{C} = 0\)
\(H_1: \mu_{A} - \mu_{C} \neq 0\)
- A vs D:
\(H_0: \mu_{A} - \mu_{D} = 0\)
\(H_1: \mu_{A} - \mu_{D} \neq 0\)
- A vs E:
\(H_0: \mu_{A} - \mu_{E} = 0\)
\(H_1: \mu_{A} - \mu_{E} \neq 0\)
- B vs C:
\(H_0: \mu_{B} - \mu_{C} = 0\)
\(H_1: \mu_{B} - \mu_{C} \neq 0\)
- B vs D:
\(H_0: \mu_{B} - \mu_{D} = 0\)
\(H_1: \mu_{B} - \mu_{D} \neq 0\)
- B vs E:
\(H_0: \mu_{B} - \mu_{E} = 0\)
\(H_1: \mu_{B} - \mu_{E} \neq 0\)
- C vs D:
\(H_0: \mu_{C} - \mu_{D} = 0\)
\(H_1: \mu_{C} - \mu_{D} \neq 0\)
- C vs E:
\(H_0: \mu_{C} - \mu_{E} = 0\)
\(H_1: \mu_{C} - \mu_{E} \neq 0\)
- D vs E:
\(H_0: \mu_{D} - \mu_{E} = 0\)
\(H_1: \mu_{D} - \mu_{E} \neq 0\)
Prueba de HSD (Honestamente significativa -> Tukey)
agricolae::HSD.test(modelo.dcl, trt = "trt", alpha = 0.05,
group = TRUE, main = NULL, console = TRUE)
Study: modelo.dcl ~ "trt"
HSD Test for rdt
Mean Square Error: 4.719243
trt, means
rdt std r Min Max
A 47.134 2.840129 5 42.26 49.43
B 51.718 5.324328 5 44.41 57.31
C 55.728 2.229747 5 53.72 59.45
D 59.168 2.065798 5 55.87 60.89
E 58.878 1.710181 5 55.87 60.17
Alpha: 0.05 ; DF Error: 12
Critical Value of Studentized Range: 4.50771
Minimun Significant Difference: 4.379324
Treatments with the same letter are not significantly different.
rdt groups
D 59.168 a
E 58.878 a
C 55.728 ab
B 51.718 b
A 47.134 cagricolae::HSD.test(modelo.dcl, trt = "trt", alpha = 0.05,
group = FALSE, main = NULL, console = TRUE)
Study: modelo.dcl ~ "trt"
HSD Test for rdt
Mean Square Error: 4.719243
trt, means
rdt std r Min Max
A 47.134 2.840129 5 42.26 49.43
B 51.718 5.324328 5 44.41 57.31
C 55.728 2.229747 5 53.72 59.45
D 59.168 2.065798 5 55.87 60.89
E 58.878 1.710181 5 55.87 60.17
Alpha: 0.05 ; DF Error: 12
Critical Value of Studentized Range: 4.50771
Comparison between treatments means
difference pvalue signif. LCL UCL
A - B -4.584 0.0388 * -8.963324 -0.2046756
A - C -8.594 0.0003 *** -12.973324 -4.2146756
A - D -12.034 0.0000 *** -16.413324 -7.6546756
A - E -11.744 0.0000 *** -16.123324 -7.3646756
B - C -4.010 0.0786 . -8.389324 0.3693244
B - D -7.450 0.0012 ** -11.829324 -3.0706756
B - E -7.160 0.0017 ** -11.539324 -2.7806756
C - D -3.440 0.1539 -7.819324 0.9393244
C - E -3.150 0.2126 -7.529324 1.2293244
D - E 0.290 0.9995 -4.089324 4.6693244Nota: Todos aquellos tratamientos que compartan por lo menos una letra serán estadísticamente similares.
Recomendación: Se debe usar la prueba de Tukey cuando como máximo se tenga 6 tratamientos.
Prueba de Duncan
agricolae::duncan.test(modelo.dcl, trt = "trt",
alpha = 0.05, group = TRUE,
main = NULL, console = TRUE)
Study: modelo.dcl ~ "trt"
Duncan's new multiple range test
for rdt
Mean Square Error: 4.719243
trt, means
rdt std r Min Max
A 47.134 2.840129 5 42.26 49.43
B 51.718 5.324328 5 44.41 57.31
C 55.728 2.229747 5 53.72 59.45
D 59.168 2.065798 5 55.87 60.89
E 58.878 1.710181 5 55.87 60.17
Alpha: 0.05 ; DF Error: 12
Critical Range
2 3 4 5
2.993547 3.133384 3.218110 3.274185
Means with the same letter are not significantly different.
rdt groups
D 59.168 a
E 58.878 a
C 55.728 b
B 51.718 c
A 47.134 dagricolae::duncan.test(modelo.dcl, trt = "trt",
alpha = 0.05, group = FALSE,
main = NULL, console = TRUE)
Study: modelo.dcl ~ "trt"
Duncan's new multiple range test
for rdt
Mean Square Error: 4.719243
trt, means
rdt std r Min Max
A 47.134 2.840129 5 42.26 49.43
B 51.718 5.324328 5 44.41 57.31
C 55.728 2.229747 5 53.72 59.45
D 59.168 2.065798 5 55.87 60.89
E 58.878 1.710181 5 55.87 60.17
Comparison between treatments means
difference pvalue signif. LCL UCL
A - B -4.584 0.0059 ** -7.577547 -1.5904531
A - C -8.594 0.0001 *** -11.727384 -5.4606157
A - D -12.034 0.0000 *** -15.308185 -8.7598153
A - E -11.744 0.0000 *** -14.962110 -8.5258900
B - C -4.010 0.0129 * -7.003547 -1.0164531
B - D -7.450 0.0003 *** -10.668110 -4.2318900
B - E -7.160 0.0003 *** -10.293384 -4.0266157
C - D -3.440 0.0339 * -6.573384 -0.3066157
C - E -3.150 0.0407 * -6.143547 -0.1564531
D - E 0.290 0.8364 -2.703547 3.2835469Nota: La prueba de Duncan usa múltiples valores críticos.
Recomendación: No usar la prueba de Duncan cuando se presentan resultados con múltiples tratamientos que obtengan varias significancias.
Prueba de Student - Newman -Keuls
agricolae::SNK.test(modelo.dcl, trt = "trt",
alpha = 0.05, group = TRUE,
main = NULL, console = TRUE)
Study: modelo.dcl ~ "trt"
Student Newman Keuls Test
for rdt
Mean Square Error: 4.719243
trt, means
rdt std r Min Max
A 47.134 2.840129 5 42.26 49.43
B 51.718 5.324328 5 44.41 57.31
C 55.728 2.229747 5 53.72 59.45
D 59.168 2.065798 5 55.87 60.89
E 58.878 1.710181 5 55.87 60.17
Alpha: 0.05 ; DF Error: 12
Critical Range
2 3 4 5
2.993547 3.665471 4.079077 4.379324
Means with the same letter are not significantly different.
rdt groups
D 59.168 a
E 58.878 a
C 55.728 a
B 51.718 b
A 47.134 cagricolae::SNK.test(modelo.dcl, trt = "trt",
alpha = 0.05, group = FALSE,
main = NULL, console = TRUE)
Study: modelo.dcl ~ "trt"
Student Newman Keuls Test
for rdt
Mean Square Error: 4.719243
trt, means
rdt std r Min Max
A 47.134 2.840129 5 42.26 49.43
B 51.718 5.324328 5 44.41 57.31
C 55.728 2.229747 5 53.72 59.45
D 59.168 2.065798 5 55.87 60.89
E 58.878 1.710181 5 55.87 60.17
Comparison between treatments means
difference pvalue signif. LCL UCL
A - B -4.584 0.0059 ** -7.577547 -1.5904531
A - C -8.594 0.0001 *** -12.259471 -4.9285291
A - D -12.034 0.0000 *** -16.413324 -7.6546756
A - E -11.744 0.0000 *** -15.823077 -7.6649232
B - C -4.010 0.0129 * -7.003547 -1.0164531
B - D -7.450 0.0008 *** -11.529077 -3.3709232
B - E -7.160 0.0006 *** -10.825471 -3.4945291
C - D -3.440 0.0666 . -7.105471 0.2254709
C - E -3.150 0.0407 * -6.143547 -0.1564531
D - E 0.290 0.8364 -2.703547 3.2835469Prueba de Least significant difference
agricolae::LSD.test(modelo.dcl, trt = "trt",
alpha = 0.05, group = TRUE,
main = NULL, console = TRUE)
Study: modelo.dcl ~ "trt"
LSD t Test for rdt
Mean Square Error: 4.719243
trt, means and individual ( 95 %) CI
rdt std r LCL UCL Min Max
A 47.134 2.840129 5 45.01724 49.25076 42.26 49.43
B 51.718 5.324328 5 49.60124 53.83476 44.41 57.31
C 55.728 2.229747 5 53.61124 57.84476 53.72 59.45
D 59.168 2.065798 5 57.05124 61.28476 55.87 60.89
E 58.878 1.710181 5 56.76124 60.99476 55.87 60.17
Alpha: 0.05 ; DF Error: 12
Critical Value of t: 2.178813
least Significant Difference: 2.993547
Treatments with the same letter are not significantly different.
rdt groups
D 59.168 a
E 58.878 a
C 55.728 b
B 51.718 c
A 47.134 dagricolae::LSD.test(modelo.dcl, trt = "trt",
alpha = 0.05, group = FALSE,
main = NULL, console = TRUE)
Study: modelo.dcl ~ "trt"
LSD t Test for rdt
Mean Square Error: 4.719243
trt, means and individual ( 95 %) CI
rdt std r LCL UCL Min Max
A 47.134 2.840129 5 45.01724 49.25076 42.26 49.43
B 51.718 5.324328 5 49.60124 53.83476 44.41 57.31
C 55.728 2.229747 5 53.61124 57.84476 53.72 59.45
D 59.168 2.065798 5 57.05124 61.28476 55.87 60.89
E 58.878 1.710181 5 56.76124 60.99476 55.87 60.17
Alpha: 0.05 ; DF Error: 12
Critical Value of t: 2.178813
Comparison between treatments means
difference pvalue signif. LCL UCL
A - B -4.584 0.0059 ** -7.577547 -1.590453
A - C -8.594 0.0000 *** -11.587547 -5.600453
A - D -12.034 0.0000 *** -15.027547 -9.040453
A - E -11.744 0.0000 *** -14.737547 -8.750453
B - C -4.010 0.0129 * -7.003547 -1.016453
B - D -7.450 0.0002 *** -10.443547 -4.456453
B - E -7.160 0.0002 *** -10.153547 -4.166453
C - D -3.440 0.0277 * -6.433547 -0.446453
C - E -3.150 0.0407 * -6.143547 -0.156453
D - E 0.290 0.8364 -2.703547 3.283547Paquete ExpDes
Diseño completamente al azar
crd.sum <- crd(
treat = data$trt,
resp = data$rdt,
quali = TRUE,
mcomp = "ccF",
nl = FALSE,
hvar = "levene",
sigT = 0.05,
sigF = 0.05,
unfold = NULL
)------------------------------------------------------------------------
Analysis of Variance Table
------------------------------------------------------------------------
DF SS MS Fc Pr>Fc
Treatament 4 522.30 130.574 13.439 1.7811e-05
Residuals 20 194.32 9.716
Total 24 716.61
------------------------------------------------------------------------
CV = 5.72 %
------------------------------------------------------------------------
Shapiro-Wilk normality test
p-value: 0.6338902
According to Shapiro-Wilk normality test at 5% of significance, residuals can be considered normal.
------------------------------------------------------------------------
------------------------------------------------------------------------
Homogeneity of variances test
p-value: 0.1038307
According to the test of levene at 5% of significance, residuals can be considered homocedastic.
------------------------------------------------------------------------
Test of Calinski & Corsten based on F distribution
------------------------------------------------------------------------
Groups Treatments Means
4 a D 59.168
5 a E 58.878
3 a C 55.728
2 b B 51.718
1 b A 47.134
------------------------------------------------------------------------Diseño de bloques completos al azar
dbca.sum <- rbd(
treat = data$trt,
resp = data$rdt,
block = data$`F`,
quali = TRUE,
mcomp = "tukey",
nl = FALSE,
hvar = "oneillmathews",
sigT = 0.05,
sigF = 0.05,
unfold = NULL
)------------------------------------------------------------------------
Analysis of Variance Table
------------------------------------------------------------------------
DF SS MS Fc Pr>Fc
Treatament 4 522.30 130.574 21.9656 0.0000025
Block 4 99.20 24.801 4.1721 0.0167511
Residuals 16 95.11 5.944
Total 24 716.61
------------------------------------------------------------------------
CV = 4.47 %
------------------------------------------------------------------------
Shapiro-Wilk normality test
p-value: 0.4781707
According to Shapiro-Wilk normality test at 5% of significance, residuals can be considered normal.
------------------------------------------------------------------------
------------------------------------------------------------------------
Homogeneity of variances test
p-value: 0.02089805
WARNING: at 5% of significance, residuals can not be considered homocedastic!
------------------------------------------------------------------------
Tukey's test
------------------------------------------------------------------------
Groups Treatments Means
a D 59.168
a E 58.878
ab C 55.728
bc B 51.718
c A 47.134
------------------------------------------------------------------------Diseño cuadrado latino
dcl.sum <- latsd(
treat = data$trt,
resp = data$rdt,
row = data$`F`,
column = data$C,
quali = TRUE,
mcomp = "sk",
sigT = 0.05,
sigF = 0.05,
unfold = NULL
)------------------------------------------------------------------------
Analysis of Variance Table
------------------------------------------------------------------------
DF SS MS Fc Pr>Fc
Treatament 4 522.30 130.574 27.6685 0.000006
Row 4 99.20 24.801 5.2553 0.011101
Column 4 38.48 9.620 2.0385 0.152720
Residuals 12 56.63 4.719
Total 24 716.61
------------------------------------------------------------------------
CV = 3.98 %
------------------------------------------------------------------------
Shapiro-Wilk normality test
p-value: 0.6922026
According to Shapiro-Wilk normality test at 5% of significance, residuals can be considered normal.
------------------------------------------------------------------------
Scott-Knott test
------------------------------------------------------------------------
Groups Treatments Means
1 a D 59.168
2 a E 58.878
3 b C 55.728
4 c B 51.718
5 d A 47.134
------------------------------------------------------------------------Prueba de Scoott-Knott
Pruebas no paramétricas
Prueba de Kruskal Wallis
Es aplicable para resultados obtenidos de un DCA.
Requiere del supuesto de que los tratamientos provienen de una misma distribución o tienen distribuciones similares.
Se observa que cada método posee una distribución distinta del resto de distribuciones de los métodos.
\(H_0: \text{Las observaciones de los métodos provienen de la misma distribución}\)
\(H_1: \text{Las observaciones de los métodos no provienen de la misma distribución}\)
Anderson-Darling k-sample test.
Number of samples: 3
Sample sizes: 34, 34, 34
Number of ties: 64
Mean of Anderson-Darling Criterion: 2
Standard deviation of Anderson-Darling Criterion: 1.05185
T.AD = ( Anderson-Darling Criterion - mean)/sigma
Null Hypothesis: All samples come from a common population.
AD T.AD asympt. P-value
version 1: 54.23 49.66 1.150e-30
version 2: 54.60 49.98 5.614e-31Conclusión: A un nivel de significancia de 0.05, se concluye que existe suficiente evidencia estadística para rechazar la hipótesis nula. Por lo tanto, las observaciones de los métodos no provienen de la misma distribución.
Recomendación: En base a la evidencia, no se recomienda usar la prueba de Kruskall Wallis.
$statistics
Chisq Df p.chisq
25.62884 3 1.140573e-05
$parameters
test p.ajusted name.t ntr alpha
Kruskal-Wallis none method 4 0.05
$means
observation rank std r Min Max Q25 Q50 Q75
1 90.55556 21.83333 3.643869 9 83 96 89.00 91.0 92.00
2 86.40000 15.30000 3.777124 10 81 91 83.25 86.0 89.75
3 95.71429 29.57143 3.638419 7 91 101 93.50 95.0 98.00
4 79.87500 4.81250 1.726888 8 77 82 78.75 80.5 81.00
$comparison
NULL
$groups
observation groups
3 29.57143 a
1 21.83333 b
2 15.30000 c
4 4.81250 d
attr(,"class")
[1] "group"comparison<-with(corn,
kruskal(observation,
method,
p.adj="bon",
group=FALSE,
main="corn"))
comparison$statistics
Chisq Df p.chisq
25.62884 3 1.140573e-05
$parameters
test p.ajusted name.t ntr alpha
Kruskal-Wallis bonferroni method 4 0.05
$means
observation rank std r Min Max Q25 Q50 Q75
1 90.55556 21.83333 3.643869 9 83 96 89.00 91.0 92.00
2 86.40000 15.30000 3.777124 10 81 91 83.25 86.0 89.75
3 95.71429 29.57143 3.638419 7 91 101 93.50 95.0 98.00
4 79.87500 4.81250 1.726888 8 77 82 78.75 80.5 81.00
$comparison
Difference pvalue Signif. LCL UCL
1 - 2 6.533333 0.0426 * 0.1474712 12.9191955
1 - 3 -7.738095 0.0238 * -14.7422174 -0.7339731
1 - 4 17.020833 0.0000 *** 10.2674375 23.7742292
2 - 3 -14.271429 0.0000 *** -21.1206220 -7.4222351
2 - 4 10.487500 0.0006 *** 3.8949224 17.0800776
3 - 4 24.758929 0.0000 *** 17.5658367 31.9520205
$groups
NULL
attr(,"class")
[1] "group"Prueba de la mediana
The Median Test for observation ~ method
Chi Square = 17.54306 DF = 3 P.Value 0.00054637
Median = 89
Median r Min Max Q25 Q75
1 91.0 9 83 96 89.00 92.00
2 86.0 10 81 91 83.25 89.75
3 95.0 7 91 101 93.50 98.00
4 80.5 8 77 82 78.75 81.00
Post Hoc Analysis
Groups according to probability of treatment differences and alpha level.
Treatments with the same letter are not significantly different.
observation groups
3 95.0 a
1 91.0 b
2 86.0 b
4 80.5 c Median r Min Max Q25 Q75
1 91.0 9 83 96 89.00 92.00
2 86.0 10 81 91 83.25 89.75
3 95.0 7 91 101 93.50 98.00
4 80.5 8 77 82 78.75 81.00
The Median Test for observation ~ method
Chi Square = 17.54306 DF = 3 P.Value 0.00054637
Median = 89
Median r Min Max Q25 Q75
1 91.0 9 83 96 89.00 92.00
2 86.0 10 81 91 83.25 89.75
3 95.0 7 91 101 93.50 98.00
4 80.5 8 77 82 78.75 81.00
Post Hoc Analysis
median chisq pvalue signif.
1 and 2 89.0 2.554444 0.1100
1 and 3 92.5 6.349206 0.0117 *
1 and 4 83.0 13.432099 0.0002 ***
2 and 3 91.0 13.246753 0.0003 ***
2 and 4 82.5 14.400000 0.0001 ***
3 and 4 82.0 15.000000 0.0001 ***Prueba de Friedman
'data.frame': 48 obs. of 3 variables:
$ judge : int 1 2 3 4 5 6 7 8 9 10 ...
$ trt : Factor w/ 4 levels "t1","t2","t3",..: 1 1 1 1 1 1 1 1 1 1 ...
$ evaluation: num 4 4 3 3 4 2 1 2 3.5 4 ...Y <- grass$evaluation
tratamiento <- grass$trt
bloque <- grass$judge
Anp <- friedman(
judge = bloque,
trt = tratamiento,
evaluation = Y,
alpha=0.05,
group=TRUE,
console=TRUE,
main=NULL)
Study: Y ~ bloque + tratamiento
tratamiento, Sum of the ranks
Y r
t1 38.0 12
t2 23.5 12
t3 24.5 12
t4 34.0 12
Friedman's Test
===============
Adjusted for ties
Critical Value: 8.097345
P.Value Chisq: 0.04404214
F Value: 3.192198
P.Value F: 0.03621547
Post Hoc Analysis
Alpha: 0.05 ; DF Error: 33
t-Student: 2.034515
LSD: 11.48168
Treatments with the same letter are not significantly different.
Sum of ranks groups
t1 38.0 a
t4 34.0 ab
t3 24.5 b
t2 23.5 bMétodos Estadísticos para Experimentos Agrícolas en R